정보처리학회논문지A (The KIPS Transactions:PartA)

한국정보처리학회 (Korea Information Processing Society)
권호 표지
DOI QR코드

DOI QR Code

상호연결망 HCN(n, n)의 고장허용도 및 HCN(n, n)과 HFN(n, n) 사이의 임베딩

The Fault Tolerance of Interconnection Network HCN(n, n) and Embedding between HCN(n, n) and HFN(n, n)

  • 이형옥 (순천대학교 컴퓨터과학과) ;
  • 김종석 (순천대학교 대학원 컴퓨터과학과)
  • 발행 : 2002.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

임베딩은 어떤 상호연결망 G를 다른 상호연결망 H에 사상시키는 것으로 연결망 G에서 개발된 알고리즘을 다른 연결망 H에서 시뮬레이션 할 수 있게 한다. 본 논문에서는 먼저 Hierarchical Cubic Network HCN(n, n) and Hierarchical Folded-hypercube Network HFN(n, n) 사이의 임베딩 방법을 제시한다. HCN(n, n)과 HFN(n, n)은 하이퍼큐브에서 제안된 성질을 가지면서 하이퍼큐브의 망비용 (분지수$\times$지름)을 개선한 상호연결망이다. HCN(n, n)은 HFN(n, n)에 연장율 3, 밀집율 2로 임베딩되고 평균연장율이 2 이하임을 보인다. HFN（n, n）은 HCN（n, n）에 연장율 0(n)에 임베딩 되지만, 평균연장율이 2 이하임을 보인다. 마지막으로 HCN（n, n）의 고장허용도에 대해 논하고, HCN（n, n）이 최대 고장 허용도(maximally fault tolerant)를 가짐을 보인다.

Embedding is a mapping an interconnection network G to another interconnection network H. If a network G can be embedded to another network H, algorithms developed on G can be simulated on H. In this paper, we first propose a method to embed between Hierarchical Cubic Network HCN(n, n) and Hierarchical Folded-hypercube Network HFN(n, n). HCN(n, n) and HFN(n, n) are graph topologies having desirable properties of hypercube while improving the network cost, defined as degree${\times}$diameter, of Hypercube. We prove that HCN(n, n) can be embedded into HFN(n, n) with dilation 3 and congestion 2, and the average dilation is less than 2. HFN(n, n) can be embedded into HCN(n, n) with dilation 0 (n), but the average dilation is less than 2. Finally, we analyze the fault tolerance of HCN(n, n) and prove that HCN(n, n) is maximally fault tolerant.

키워드

참고문헌

  1. S. B. Akers and B. Krishnamurthy, 'On Group Graphs and Their Fatult Tolerance,' IEEE Trans. Comput., Vol.c-36, No.7, pp.885-888, July, 1987 https://doi.org/10.1109/TC.1987.1676983
  2. S. B. Akers and B. Krishnamurthy, 'A Group-Theoretic Model for Symmertric Interconnection Network,' IEEE Trans. Comput., Vol.38, No.4, pp.555-565, 1989 https://doi.org/10.1109/12.21148
  3. W. J. Dally, 'Virtual-Channel Flow Control,' IEEE Trans. Parallel and Distributed Systems, Vol.3, No.2, pp.194-205, March, 1992 https://doi.org/10.1109/71.127260
  4. K. W. Doty, 'New Designs for Dense Processor Interconnection Networks,' IEEE Trans. Computer., Vol.c-33, No.5, May, 1984 https://doi.org/10.1109/TC.1984.1676461
  5. D. R. Duh, G. H. Chen and J. F. Fang, 'Algorithms and Properties of a New Two-Level Network with Folded Hypercubes as Basic Modules,' IEEE Trans. Parallel Distributed syst., Vol.6, No.7, pp.714-723, 1995 https://doi.org/10.1109/71.395400
  6. A. EI-Amawy and S. Latifi, 'Properties and Performance of Folded Hypercubes,' IEEE Trans. Parallel Distributed syst., Vol.2, No.1, pp.31-42, 1991 https://doi.org/10.1109/71.80187
  7. T-Y. Feng, 'A Survey of Interconnection Networks,' IEEE Computer, pp.12-27, December, 1981 https://doi.org/10.1109/C-M.1981.220290
  8. K. Ghose and K. R. Desai, 'Hierarchical Cubic Networks,' IEEE Trans. Parallel Distributed syst., Vol.6, No.4, pp.427-436, 1995 https://doi.org/10.1109/71.372797
  9. F. Harary, J. P. Hayes, and H-J.WU, 'A Survey of the Theory of Hypercube Graphs,' Comput. Math. Appl., Vol.15, pp.277-289, 1988 https://doi.org/10.1016/0898-1221(88)90213-1
  10. K. Hwang and F. A. Briggs, Computer Architecture and Parallel Processing, 4th Printing, MacGraw-Hill International Editons, New York, 1988
  11. F. T. Leighton, Introduction to Parallel Algorithms and Architectures : Arrays, Hypercubes, Morgan Kaufmann Publishers, 1992
  12. V. E. Mendia and D. Sarkar, 'Optimal Broadcasting on the Star Graph,' IEEE Trans. Parallel Distributed syst., Vol.3, No.4, pp.389-396, 1992 https://doi.org/10.1109/71.149958
  13. J-H.Park, Circulant Graphs and Their Application to Communication Networks, Ph.D.Thesis, Dept. of Computer Science, KAIST, Taejon Korea, 1992
  14. D. A. Reed and R. M. Fujimoth, Multicomputer Networks : Message-Based Parallel Processing, MIT Press, 1987
  15. A. S. Vaidya, P. S. N. Rao and S. R. Shankar, 'A Class of Hypercube_like Networks,' Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing, pp.800-803, Dec., 1993 https://doi.org/10.1109/SPDP.1993.395450
  16. P. Wiley, 'A Parallel Architecture Comes of Age at Last,' IEEE Spectrum, Vol.24, pp.46-50, 1987
  17. A. Y. Wu, 'Embedding of Tree Networks into Hypercubes,' J. Parallel and Distributed Computing, Vol.2, pp.238-249, 1985 https://doi.org/10.1016/0743-7315(85)90026-7
  18. S-K.Yun and K-H.Park, 'Comments on'Hierarchical Cubic Networks,' IEEE Trans. Parallel Distributed syst., Vol.9, No.4, pp.410-414, 1998 https://doi.org/10.1109/71.667900